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Probabilistic And Statistical methods for Cosmological AppLications

Final Report Summary - PASCAL (Probabilistic And Statistical methods for Cosmological AppLications)

The project has been concerned with the development of probabilistic and statistical techniques for cosmological data analysis, focussing in particular on spherical random fields. As such, it was truly interdisciplinary in every aspects - indeed the postdocs that were hired are almost equally split between some with a mathematical/statistical background and other which hold degrees in cosmology and astrophysics. Publications were also largely split between mathematical and statistical journals (including for instance Geometric and Functional Analysis, Comm.Math.Phys. J. Functional Analysis, Annals of Probability, Annals of Applied Probability, J.Geometric Analysis, J.Math.An.Appl. Applied and Computational Harmonic Analysis, Bernoulli, Ann.Inst.H.Poinc. Stochastic Processes and their Applications) and journals which are strictly addressed to an audience of physicists (i.e. Mon.Not.Royal,Astr.Soc. J.Cosm.Astropart.Physics Astrophysical Journal, Astronomy and Astrophysics). Components of Pascal have also contributed significantly to the analysis of CMB data from the Planck Satellite Mission by the European Space Agency. Many collaborations among postdocs with different backgrounds have grown out of the project, producing alternate point of views on classical and novel research challenges.

A number of novel techniques which were developed within this project have already been applied to cosmological data, especially CMB - in particular, novel estimation techniques for nonlinearity parameters and nonGaussianity, geometric functionals on wavelet/needlet components to search for asymmetries and anisotropies, multiple testing schemes based upon analytic results on critical points distributions. Other findings have drawn quite a lot of interest also from the point of view of pure mathematics: in particular, very neat and explicit formulae were derived for the asymptotic variances and distribution for geometric functionals evaluated on the excursion sets of Gaussian spherical eigenfunctions.

To stress these interdisciplinary aspects, a major intedisciplinary event was organized in Rome, featuring world class researchers working in Stochastic Processes, RandomFields and Geometry (i.e. R.Adler N.Leonenko J.Taylor G.Peccati A.Schwartzman I.Wigman) mathematical statisticians working on nonparametric and harmonic-based methods (including A. Dalalyan,C.Genovese J.Jin R.Nickl I.Pesenson L.Wasserman) and top class physicists with a leading role in cosmological data analysis (including A.Balbi S.Feeney S.Matarrese J.McEwen R.Scaramella J.-L. Starck, B.Wandelt,); see

Many ideas that have originated during this project are characterized by strong ongoing research; to mention just one area, a lot of work is currently going on by former project members at the intersection between the the Geometry of Spherical Random Fields and the analysis of Cosmological data. We hence hope that Pascal will leave a lasting legacy, not only in terms of results but also for its strong contribution in building up a tiny interdisciplinary research community.